Light - Reflection and Refraction

Synopsis

Nature of Light 

• Light enables us to see several thousands of objects every day. 
• Though light is invisible, it makes objects around us visible. 
• Light is a form of electromagnetic radiation and a non-mechanical wave. 
• Non-mechanical waves do not require a material as a medium for propagation.
• Light travels along a straight line and this property are called the rectilinear propagation. 
• This straight line is called a ray, and a bundle of rays is called a beam of light.
• Thus, real images are formed when the rays after reflection or refraction meets at a point.
• If the rays appear to meet when produced backwards, then the image formed is virtual. 
• The real image can be caught on a screen but the virtual image cannot be formed on a screen.

Reflection of Light

• When light falls on a body, it may be absorbed, may be transmitted or may return to the same medium.
• In the reflection of light, light waves are neither transmitted nor absorbed, but they are deflected from the surface of the medium back into the same medium.
• This is governed by the laws of reflection.
  
  
• First law of reflection: The incident ray, the normal to the surface at the point of incidence and the reflected ray, all lie in the same plane.
• Second law of reflection: The angle of incidence is equal to the angle of reflection.

Characteristics of the Image formed by a Plane Mirror

• The image formed by a plane mirror is always virtual and erect. 
• The size of the image is equal to the size of the object, and the image is laterally inverted. 
• The image formed by the plane mirror is as far behind the mirror as the object is in front of it.
  
  
• Similar to plane mirrors, curved mirrors also form images. Mirrors whose reflecting surfaces are spherical are known as spherical mirrors.

Refraction of Light 

• Light travelling obliquely from one medium to another undergoes a change in its direction of propagation.
• The phenomenon of change in the path of light from one medium to another is called refraction of light. 

Laws of Refraction 

• First law of refraction: The incident ray, the refracted ray and the normal to the interface of the two transparent media at the point of incidence, all lie in the same plane.
• Second law of refraction: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media and for a given wavelength of light. This law is also known as Snell’s law.
  
  
  
• The constant is called the refractive index of the second medium with respect to the first medium.
• The cause of refraction is the change in the speed of light as it goes from one medium to another medium.
• Larger the difference in speed of light, the greater will be the angle of bending and vice versa.

Refractive Index 

• The extent of the change in the direction of a light ray that takes place in a given pair of media is expressed in terms of the refractive index. 
• Light travels fastest in vacuum and also with almost the same speed in air. In other media, its speed is relatively less. The value of the refractive index for a given pair of media depends on the speed of light in the two media.
• The refractive index of medium 2 with respect to medium 1 is given as;
  
  
  
  
  
• Similarly, the refractive index of medium 1 with respect to medium 2 is
  
  
  
  
  
• If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is known as the absolute refractive index of the medium.
  
  

Spherical Mirrors

• A spherical mirror whose reflecting surface is curved outwards and polished on the inner spherical surface is a convex mirror.
• A spherical mirror whose reflecting surface is curved inwards and polished on the outer spherical surface is a concave mirror.
  
  

Image Formation by a Concave Mirror for Different Positions of an Object

 

 

 

 

 

 

 

 

 

 

 

Nature, Position and Relative Size of the Image Formed by a Convex Mirror

 

 

 

 

 

 

• Sign Convention: - 
  
  

 

Mirror Formula

• The distance of the object from the pole is called the object distance (u).
• The distance of the image from the pole is called the image distance (v).
• The distance of the principal focus from the pole is called the focal length (f).
• The object distance, the image distance and the focal length are related as
  
  

 

Magnification by Mirror

• Magnification is the ratio of the height of the image to the height of the object. It is represented by m.
  
  
  
  
• Magnification is also related to the object distance and the image distance as;
  
  
  
  
• The height of the object is taken as positive as the object is usually placed above the principal axis. The height of the image should be taken as positive for virtual images. It should be taken as negative for real images.
• Negative magnification indicates that the image is real, and positive magnification indicates that the image is virtual.

 

Spherical Lens

• A lens having both surfaces bulging outwards is called a double convex lens or simply a convex lens. A convex lens is thicker at the middle than at the edges.
• The convex lens converges the light rays incident on it to a point.
  
  
  
  
• Hence, a convex lens is also known as a converging lens.

 

A lens having both surfaces curved inwards is called a double concave lens or simply a concave lens.

 

• The concave lens diverges the light rays incident on it.
  
  

Hence, a concave lens is also known as a diverging lens. 

 

 

Image Formation by a Convex Lens for Different Positions of the Object

 

 

 

 

 

 

 

 

 

 

 

 

Nature, position and relative size of the image formed by a convex mirror

 

 

 

 

 

 

 

Sign Convention:

• The new Cartesian sign convention is same as that for spherical mirrors. 
• The difference is that the distances are measured from the optical centre.
• According to the sign convention, the focal length of a convex lens is positive and that of a concave lens is negative.

Lens Formula 

• The distance of the object from the optical centre is called the object distance (u).
• The distance of the image from the optical centre is called the image distance (v).
• The distance of the principal focus from the optical centre is called the focal length (f).
• The object distance, image distance and focal length are related as
  
  
  
  
  
• The new Cartesian sign convention is to be followed when using this formula.

 

Magnification by Lens

• Magnification produced by a lens is the ratio of the height of the image to the height of the object. It is represented as m.
  
  
  
  
  
• Magnification is also related to the object distance and the image distance as;
  
  

 

Power of a Lens

• The ability of a lens to converge or diverge light rays depends on its focal length.
• A convex lens of short focal length bends the light rays through large angles by focusing them closer to the optical centre. 
• Similarly, a concave lens of very short focal length causes higher divergence than the one with longer focal length. 
• The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power. 
• The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given as;
  
  
• The SI unit of power is dioptre (D).
• One dioptre is the power of a lens whose focal length is 1 m. 
• Thus, 1 D = 1 m⁻¹.
• The power of a convex lens is positive and that of a concave lens is negative.

 

Newton’s Corpuscular Theory

Sir Isaac Newton proposed his corpuscular theory in 17th century on the following assumptions.

• Light is made up of point-like particles called corpuscles having negligible mass.
• These particles are perfectly elastic and travel in straight lines.
• Based on the laws of motion interfaces of different optical media exert forces of attraction and repulsion leading to the phenomena of reflection and refraction.
• Speed of light is greater in a denser medium.
• The different of the corpuscles account for the different colours.

 

Huygen’s Wave Theory

• Huygens’ Principle
• According to Huygens’ principle,
  (a) Each point on the given wavefront (called primary wavefront) acts as a fresh source of new disturbance, called secondary wavelet, which travels in all directions with the velocity of light in the medium.
  (b) A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new wavefront at that instant. This is called the secondary wavefront.
• Huygens’ construction is based on the principle that every point of a wavefront is a source of a secondary wavefront. The envelope of these wavefronts, i.e., the surface tangent to all the secondary wavefront, gives the new wavefront.